Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V-mappings instead of W-ones.     

Sodium trimer ordering on a NaxCoO2 surface

Sodium ion ordering on an in situ cleaved NaxCoO2 (x=0.84) surface has been studied by ultrahigh vacuum scanning tunneling microscopy at room temperature. Three main phases, with p(3 x 3), ( radical7 x radical7), and (2 radical3 x 2 radical3) hexagonal unit cells and a surface Na concentration of 1/3, 3/7, 1/2, respectively, were identified. One surprising finding is that Na trimers act as the basic building blocks that order in long range. The stability of Na trimers is attributed to the increased Na coordination with oxygen as indicated by ab initio calculations, and possibly at finite temperature by configuration entropy.     

The effect of polymer architecture on the nano self-assemblies based on novel comb-shaped amphiphilic poly(allylamine)

Twelve novel poly(allylamine) (PAA)-based, comb-shaped amphiphilic polymers have been developed. Hydrophobic groups of cetyl, palmitoyl and cholesteryl were randomly grafted to PAA and quaternisation was carried out on some modified polymers. Polymers were characterised using ¹H NMR, elemental analysis and differential scanning calorimetry. All polymers formed nano self-assemblies in the aqueous solution with a positive zeta potential and were able to encapsulate a hydrophobic agent, methyl orange, in the core. The critical aggregation concentration (CAC) and the microviscosity were found to be dependent on the polymer hydrophobicity. Being the most hydrophobic polymer, cholesteryl-grafted PAA had the lowest CAC (0.02 mg mL⁻¹) and the highest microviscosity. They appeared to form dense nanoparticles and were transformed into novel nanostructures in the presence of free cholesterol. Palmitoyl-grafted polymers formed nanoparticles while cetyl-grafted polymers formed polymeric micelles. The flexibility of cetyl chains possibly resulted in the formation of multicore polymeric micelles.     

EULERIAN–LAGRANGIAN COMPUTATIONS ON PHASE DISTRIBUTION OF TWO-PHASE BUBBLY FLOWS

A comprehensively theoretical model is developed and numerically solved to investigate the phase distribution phenomena in a two-dimensional, axisymmetric, developing, two-phase bubbly flow. The Eulerian approach treats the fluid phase as a continuum and solved Eulerian conservation equations for the liquid phase. The Lagrangian bubbles are tracked by solving the equation of motion for the gas phase. The interphase momentum changes are included in the equations. The numerical model successfully predicts detailed flow velocity profiles for both liquid and gas phases. The development of the wall-peaking phenomenon of the void fraction and velocity profiles is also characterized for the developing flow. For 42 experiments in which the mean void fraction is less than 20 per cent, numerical calculations demonstrate that the predictions agree well with Liu's experimental data. © 1997 by John Wiley & Sons, Ltd.     

Tikhonov regularization method for a system of equilibrium problems in Banach spaces

The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.     

Convergence acceleration by varying time‐step size using Bi‐CGSTAB method for turbulent flow computation

A design of varying step size approach both in time span and spatial coordinate systems to achieve fast convergence is demonstrated in this study. This method is based on the concept of minimization of residuals by the Bi‐CGSTAB algorithm, so that the convergence can be enforced by varying the time‐step size. The numerical results show that the time‐step size determined by the proposed method improves the convergence rate for turbulent computations using advanced turbulence models in low Reynolds‐number form, and the degree of improvement increases with the degree of the complexity of the turbulence models. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 454–474, 2001.     

Predicting the whiteness index of cotton fabric with a least squares model

Cellulose - The textile bleaching process that involves hot hydrogen peroxide (H2O2) solution is commonly practised in cotton fabric manufacture. The purpose of the bleaching process is to remove...     

Microsized 2D protein arrays immobilized by micro-stamps and micro-wells for disease diagnosis and drug screening

A novel method of protein array immobilization, using micro stamps to pick up proteins from micro wells and deposit them on to a bio-absorption chip, has been developed. This method can potentially transfer several protein spots on to an organized array for applications such as disease diagnosis and drug screening by parallel biological or chemical processes. Fabrication of the micro stamp and the micro well arrays involves thick-photoresist lithography, bulk micromachining, and a molding process, whereas fabrication of the bio-absorption chip involves amino-modification by use of APTS (aminopropyItrimethoxysilane) and surface activation by use of BS3 (bis-sulfosuccinimidyl suberate). Successful transfer of protein on to the bio-absorption surface using the micro stamp-well array has been demonstrated. The size variation between different stamping spots has been shown to be less than 10%, and the APTS-BS3 surface has also been proved to bind the protein efficiently. Appreciable protein retention was achieved during 6-h washing, which shows the binding strength of the bio-absorption surface is sufficient for protein processing.     

A steepest-descent Krasnosel’skii–Mann algorithm for a class of variational inequalities in Banach spaces

In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.